[geometry-ml:05128] 東大数理・複素解析幾何セミナー4/24

[Kengo Hirachi]

皆様

東大数理・複素解析幾何セミナーのお知らせです。

2023年04月24日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室
対面・オンラインのハイブリッド形式で行います。オンライン参加される場合は参考URLからご登録ください。
大沢健夫 氏 (名古屋大学)
Guan-Zhouの開性定理と
L
2
最小化積分の凹性 (日本語)
[ 講演概要 ]
Motivated by a question of approximating plurisubharmonic (=psh) functions by those with tame singularities, Demailly and Kollar asked several basic questions on the singularities of psh functions. Guan solved two of them effectively in a paper published in 2019. One of their corollaries says the following.

THEOREM. Let 
Ω
 be a pseudoconvex domain in 
C
n
 and let 
φ
 be a negative psh function on 
Ω
 such that 
∫
Ω
e
−
φ
<
∞
. Then, 
e
−
p
φ
∈
L
1
loc
 around 
x
 for any 
x
∈
Ω
 and 
p
>
1
 satisfying the inequality 
p
p
−
1
>
∫
Ω
e
−
φ
K
Ω
(
x
)
,
where 
K
Ω
 denotes the diagonalized Bergman kernel of 
Ω
.

This remarkable result is a consequence of a basic property of the minimal 
L
2
 integrals (=MLI). The main purpose of the talk is to give an outline of the proof of Theorem by explaining the relation between several notions including the MLI which measure the singularities of psh functions. It will also be mentioned that the proof of Theorem is essentially based on the optimal Ohsawa-Takegoshi type extension theorem, which leads to a concavity property of MLI. Recent papers by Guan and his students will be reviewed, too.
[ 参考URL ]
https://u-tokyo-ac-jp.zoom.us/meeting/register/tZEqceqsrTIjEtRxenSMdPogvCxlWzAogj5A
Zoom URL・ID・パスワードなどは１年間同じものを使うので登録は一度で大丈夫です．
今後の予定はこちら
https://www.ms.u-tokyo.ac.jp/seminar/geocomp/future.html

講演者も募集中です。

世話人
平地 健吾、高山 茂晴
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